How do I make my mesh have a matte black finish in cycles?
Matte simply means diffuse.  So for a pure matte, black shader I would simply use a diffuse shader with the color set to almost black (HSV about [0,0,0.98]).  If it is pure black, it will not reflect any light and thus not look good.

Photorealism note:  Almost nothing in the real world is purely diffuse.  To make your material look much better and more believable you might want to mix in (with a factor of about 0.05) of a glossy shader with a roughness of around 0.12.